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The low-signal-gain versus frequency slope is often a highly desirable property of traveling wave tube (TWT) used in a communication system. The gain ripple is usually caused by internal reflexions of forward and backward waves in the TWT. Random fabrication error may have a detrimental effect on the performance of TWT. The quartic equation including backward wave models the effect of reflection to analyze the effect of Gain ripple from many small circuit errors in a TWT operating under small-signal condition. We present a transfer matrix method (TMM) to correctly calculate the transmission and reflection of the wave incident respectively from left and right at a single isolated joint. The TMM, which links the input signal to output signal that includes the feedback signal from the reflections at multiple joints to the output end, can calculate the gain ripple of multiple internal reflections. Appling this method to several numerical examples, we look at how small signal gain is affected by a single isolated discontinuity and many small randomly distributed discontinuities. In particular, we investigate the effects of random perturbations of Pierce velocity detuning parameter b and Pierce gain parameter C on the small signal gain at different values of space charge 4QC. The computed result agrees with that from Chernin's model. We find that reflections may significantly increase the statistical effects on the gain. A further conclusion is that the standard deviation of gain, dgain, increases with b gradually, but the ratio of the backward wave power to the forward wave power at x=0 decreases with b when standard deviation of pierce velocity detuning parameter, b, is more than 1.5. In another example, the effects of two discontinuities of pitch distribution and many small random pitch errors on gain ripple are reported for a G-band TWT. We find that larger pitch error and longer distance for the discontinuities may produce a larger ripple in the small-signal-gain versus frequency. Many small discontinuities may produce a large gain ripple, and the gain ripple grows as the level of pitch error increases. These effects of random fabrication errors become increasingly important for very high frequencies, such as 1 THz, at which TWTs are currently being designed and built.
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Keywords:
- transfer matrix method /
- small signal gain /
- reflection /
- traveling wave tube
[1] Wenninger W L, Benton R T, Choi M S, Feicht J R, Hallsten U R, Limburg H C, McGeary W L, Zhai X 2005 IEEE Trans. Electron Devices 52 673
[2] Xie W Q, Wang Z C, Luo J R, Liu Q L 2014 Acta Phys. Sin. 63 044101 (in Chinese) [谢文球, 王自成, 罗积润, 刘青伦 2014 63 044101]
[3] Hu Y L, Yang Z H, Li B 2010 Acta Phys. Sin. 59 5439 (in Chinese) [胡玉禄, 杨中海, 李斌 2010 59 5439]
[4] He J, Huang M G, Li X X, Li H Q, Zhao L, Zhao J D, Li Y, Zhao S L 2015 Chin. Phys. B 24 104102
[5] Yi H X, Xiao L, Liu P K, Hao B L, Li F, Li G C 2011 Acta Phys. Sin. 60 068403 (in Chinese) [易红霞, 肖刘, 刘濮鲲, 郝保良, 李飞, 李国超 2011 60 068403]
[6] Wallander S O 1972 IEEE Trans. Electron Devices 19 655
[7] Pengvanich P, Chernin D, Lau Y Y, Luginsland J W, Gilgenbach R M 2008 IEEE Trans. Electron Devices 55 916
[8] Sengele S, Barsanti M L, Hargrave T A, Armstrong C M, Booske J H, Lau Y Y 2013 J. Appl. Phys. 113 074905
[9] Sengele S 2012 Ph. D. Dissertation (Madison: University of Wisconsin-Madison)
[10] Rittersdorf I M, Antonsen T M, Chernin D, Lau Y Y 2013 IEEE Trans. Electron Devices 1 117
[11] Chernin D, Rittersdorf I, Lau Y Y, Antonsen T M, Levush B 2012 IEEE Trans. Electron Devices 59 1542
[12] Pendry J B 1994 J. Mod. Opt. 41 209
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[1] Wenninger W L, Benton R T, Choi M S, Feicht J R, Hallsten U R, Limburg H C, McGeary W L, Zhai X 2005 IEEE Trans. Electron Devices 52 673
[2] Xie W Q, Wang Z C, Luo J R, Liu Q L 2014 Acta Phys. Sin. 63 044101 (in Chinese) [谢文球, 王自成, 罗积润, 刘青伦 2014 63 044101]
[3] Hu Y L, Yang Z H, Li B 2010 Acta Phys. Sin. 59 5439 (in Chinese) [胡玉禄, 杨中海, 李斌 2010 59 5439]
[4] He J, Huang M G, Li X X, Li H Q, Zhao L, Zhao J D, Li Y, Zhao S L 2015 Chin. Phys. B 24 104102
[5] Yi H X, Xiao L, Liu P K, Hao B L, Li F, Li G C 2011 Acta Phys. Sin. 60 068403 (in Chinese) [易红霞, 肖刘, 刘濮鲲, 郝保良, 李飞, 李国超 2011 60 068403]
[6] Wallander S O 1972 IEEE Trans. Electron Devices 19 655
[7] Pengvanich P, Chernin D, Lau Y Y, Luginsland J W, Gilgenbach R M 2008 IEEE Trans. Electron Devices 55 916
[8] Sengele S, Barsanti M L, Hargrave T A, Armstrong C M, Booske J H, Lau Y Y 2013 J. Appl. Phys. 113 074905
[9] Sengele S 2012 Ph. D. Dissertation (Madison: University of Wisconsin-Madison)
[10] Rittersdorf I M, Antonsen T M, Chernin D, Lau Y Y 2013 IEEE Trans. Electron Devices 1 117
[11] Chernin D, Rittersdorf I, Lau Y Y, Antonsen T M, Levush B 2012 IEEE Trans. Electron Devices 59 1542
[12] Pendry J B 1994 J. Mod. Opt. 41 209
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